Solving Notation Confusion in Law's Combustion Physics

[Saladsamurai]

I am reading through a combustion physics text by Law and I am a little confused by this notation for a reaction. He says:

Consider a chemical reaction given by

$$\sum_{i=1}^N\nu_i'M_i\leftrightharpoons\sum_{i=1}^N\nu_i''M_i$$

where M_i is the chemical symbol for the i^th species and $\nu_i$ the corresponding molar concentration coefficient ...

My questions:

1) In this sense, is the "concentration" v_i the same as the relative composition? That is, is it simply the "mole fraction?"

2) Both of the summands in the reactants and products run from i = 1 to N. I do not understand this. It seems that this would not allow for the formation of different molecules in the products. That is, it assumes that the reactants and the products are identical. But in the case of a simple reaction like $CO + \frac{1}{2}O_2 \leftrightharpoons CO_2$ it is clear that there are 1) a different number of products than reactants and 2) the subscript "1" in the reactants is not representative of the same molecule as "1" in the products.Is it possible that this reaction is being written "atom wise" (I have never heard of this) instead of as molecules? Or is it that the indices on the left hand side and those on the right hand side are completely independent? That is, the set of "N" molecules in the reactants is a completely different set than the "N" molecules in the products?

 

[Ygggdrasil]

I'll address your second question first. It's probably more correct to write the equation as:
$$\sum_{i=1}^N\nu_i\prime R_i\leftrightharpoons\sum_{i=1}^N\nu_i\prime\prime P_i$$
With R representing the reactants and P representing the products.

For your first question, the v_i do not represent concentrations nor do they represent mole fractions. They are most correctly referred to as stoichiometric coefficients and simply represent the molar ratios of reactants required and products created by the reaction. In your example of CO + 1/2 O₂ --> CO₂, the v_i are 1, 1/2, and 1.

 

[Saladsamurai]

I'll address your second question first. It's probably more correct to write the equation as:
$$\sum_{i=1}^N\nu_i' R_i \leftrightharpoons \sum_{i=1}^ N \nu_i'' P_i$$
With R representing the reactants and P representing the products.

For your first question, the v_i do not represent concentrations nor do they represent mole fractions. They are most correctly referred to as stoichiometric coefficients and simply represent the molar ratios of reactants required and products created by the reaction. In your example of CO + 1/2 O₂ --> CO₂, the v_i are 1, 1/2, and 1.

Hmmm...You see, that is what I am used to in my other texts; however, I have quoted him word for word. He distinctly uses the word "concentrations." And he has made no distinction that the different M's are "R" and "P" as you have. I'll assume that it is just poor notation, but surely the use of the word "concentrations" was intentional (?).

Thanks,
Casey

 

[Ygggdrasil]

I'd say it's probably all just poor notation and wording.

 

[Saladsamurai]

I guess I can live with that. Thanks for your response.

~Casey